1. I solved my Lag problems by ignoring party/clan based game modes.
2. I agree, it must be a bug or something. Hope they fix this soon.
3. Thats because he has a lower ping to Host then you, its not your fault either.
4. Haven't experienced it yet.
Overall i find Black Ops 2 to be the best Call of Duty ever made, no game is ever perfect but this game is near close to being perfect. No noob tubes, no commando, no ghost campers, no assassin campers, no op killstreaks, no op perks. Love it.